Theorem mulcomi 8280

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
mulcomi	|- ( A x. B ) = ( B x. A )

Proof of Theorem mulcomi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcom 8256	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )
4	1, 2, 3	mp2an 426	1 |- ( A x. B ) = ( B x. A )

Syntax hints:   = wceq 1398   e. wcel 2203  (class class class)co 6050   CCcc 8125   x. cmul 8132

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-mulcom 8228

This theorem is referenced by:  mulcomli  8281  8th4div3  9457  numma2c  9754  nummul2c  9758  9t11e99  9838  binom2i  11010  fac3  11094  tanval2ap  12399  pockthi  13056  decsplit1  13126  decsplit  13127  sincosq4sgn  15694  2logb9irrALT  15839  2lgsoddprmlem2  15979  2lgsoddprmlem3d  15983